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MATHEMATICS
Irreducible characters of the icosahedral group
S. Kanemitsua, Jay Mehtab, Y. Sunc a Sanmenxia SUDA New Energy Research Institute, Sanmenxia, Henan, P. R. China
b Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar, Gujarat, India
c Graduate School of Engrg., Kyushu Inst. Tech., 1-1Sensuicho Tobata, Kitakyushu, Japan
Abstract:
To study point groups, their irreducible characters are essential. The table of irreducible characters of the icosahedral group $A_5$ is usually obtained by using its duality to the dodecahedral group. It seems that there is no literature which gives a routine computational way to complete it. In the works of Harter and Allen, a computational method is given and the character table up to the tetrahedral group $A_4$ using the group algebra table and linear algebra. In this paper, we employ their method with the aid of computer programming to complete the table. The method is applicable to any other more complicated groups.
Keywords:
icosahedral group, irreducible representation, simple characters, regular representation, eigenvalues.
Received: 11.08.2023 Revised: 15.08.2023 Accepted: 16.08.2023
Citation:
S. Kanemitsu, Jay Mehta, Y. Sun, “Irreducible characters of the icosahedral group”, Nanosystems: Physics, Chemistry, Mathematics, 14:4 (2023), 405–412
Linking options:
https://www.mathnet.ru/eng/nano1204 https://www.mathnet.ru/eng/nano/v14/i4/p405
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Abstract page: | 51 | Full-text PDF : | 24 |
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